1. Field of the Invention
The present invention relates to an active inductor and, more particularly, to a cell having improved linearity by employing a linearization scheme and a structure of an active inductor using the same.
2. Description of the Related Art
FIGS. 1A and 1B are views illustrating the structure of the related art active inductor.
With reference to FIG. 1A, the related art active inductor has the structure of a gyrator-C. The gyrator-C may be implemented by connecting inputs of two amplifiers 100 to outputs of the counterparts such that they are reversed with relation to each other. FIG. 1B shows an equivalent circuit formed by adding output resistors (ro1, ro2) and capacitors (C1, C2) to the structure of FIG. 1A.
An input impedance Y(s) of the circuit illustrated in FIG. 1A may be obtained as represented by Equation 1 shown below:
                              Y          ⁡                      (            s            )                          =                              sC            2                    +                      1                          r                              o                ⁢                                                                  ⁢                2                                              +                      1                                          s                ⁢                                                      C                    1                                                                              g                                              m                        ⁢                                                                                                  ⁢                        1                                                              ⁢                                          g                                              m                        ⁢                                                                                                  ⁢                        2                                                                                                        +                              1                                                      g                                          m                      ⁢                                                                                          ⁢                      1                                                        ⁢                                      g                                          m                      ⁢                                                                                          ⁢                      2                                                        ⁢                                      r                                          o                      ⁢                                                                                          ⁢                      1                                                                                                                              [                  Equation          ⁢                                          ⁢          1                ]            
Here, gm1 and gm2 are trans-conductances of an inverting amplifier.
In comparison between Equation 1 and the equivalent circuit illustrated in FIG. 1B, an equivalent parallel resistance Rp, an equivalent parallel capacitor Cp, an equivalent serial resistance Rs, and an equivalent inductor (L) can be expressed as shown Equation below:
                                          R            p                    =                      r                          o              ⁢                                                          ⁢              2                                      ,                              C            p                    =                      C            2                          ,                                  ⁢                  L          =                                    C              1                                                      g                                  m                  ⁢                                                                          ⁢                  1                                            ⁢                              g                                  m                  ⁢                                                                          ⁢                  2                                                                    ,                              R            s                    =                      1                                          g                                  m                  ⁢                                                                          ⁢                  1                                            ⁢                              g                                  m                  ⁢                                                                          ⁢                  2                                            ⁢                              r                                  o                  ⁢                                                                          ⁢                  1                                                                                        [                  Equation          ⁢                                          ⁢          2                ]            
As noted from Equation 2, as the equivalent parallel capacitance Cp is reduced, the resonant frequency of the inductor is increased, so C2 must therefore become small. Also, when gm1 and gm2 are reduced and the value C1 is increased, the inductance of the equivalent inductor (L) is increased. Then, the equivalent serial resistance Rs would increase to degrade a Q value of the inductor (L). Thus, in order to improve this problem, resistances ro1 and ro2 must be large. Thus, a circuit in which the two resistances ro1 and ro2 are large is required, and this is made possible by using a negative resistance circuit.
FIGS. 2A and 2B are circuit diagrams of the related art negative resistance circuit.
With reference to FIG. 2A, a negative resistance circuit 200 includes two NMOSs M3 and M4 and a resistor R.
With reference to FIG. 2B, the negative resistance circuit 200 may be expressed as an equivalent circuit by using equivalent circuits (gm4V1, gm3V2) of the NMOSs M3 and M4, and input impedance Zi in this case may be represented by Equation 3 shown below:
                              Z          i                =                              -                                          R                ⁡                                  (                                                            1                                              g                                                  m                          ⁢                                                                                                          ⁢                          3                                                                                      +                                          1                                              g                                                  m                          ⁢                                                                                                          ⁢                          4                                                                                                      )                                                            R                -                                  (                                                            1                                              g                                                  m                          ⁢                                                                                                          ⁢                          3                                                                                      +                                          1                                              g                                                  m                          ⁢                                                                                                          ⁢                          4                                                                                                      )                                                              =                      R            //                          [                              -                                  (                                                            1                                              g                                                  m                          ⁢                                                                                                          ⁢                          3                                                                                      +                                          1                                              g                                                  m                          ⁢                                                                                                          ⁢                          4                                                                                                      )                                            ]                                                          [                  Equation          ⁢                                          ⁢          3                ]            
Values gm3 and gm4 are trans-conductances of the inverting amplifier, respectively.
With reference to Equation 3, a high Q value of the inductor (L) can be obtained by adjusting the resistance value R and the trans-conductance values gm3 and gm4 of the NMOSs such that the denominator term becomes 0.
FIGS. 3A and 3B show structures of the related art active inductor.
With reference to FIG. 3A, the active inductor is configured to have a structure of a gyrator-C using two differential amplification cells 300 including negative resistance and capacitors. However, the active inductor has a fatal flaw in having nonlinearity, because of the nonlinearity of the amplification cells 300.
With reference to FIG. 3B, when an input voltage swing of differential inputs (Input +/−) is increased in the amplifying circuits, the gm value of the transistor is affected. Then, a negative resistance value of an equivalent resistance in the negative resistance circuit connected to a load of a common-source amplifier using a PMOS as an active load is changed to cause the inductance (L) to be changed as noted from Equation 2, resultantly making the circuit nonlinear.